Asked by df
For an in-class demonstration, a teacher flips a fair coin 5 times, and each of the 5 times it lands on heads. A student argues that it is more likely to land on tails on the next, or 6th, flip. Is the student correct? Explain your reasoning.
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GPT-5 mini
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No — the student is incorrect (assuming the teacher really is using a fair coin).
Coin flips are independent events, so the outcome of the sixth flip does not depend on the first five. For a fair coin
- P(tail on 6th | first five were heads) = P(tail on 6th) = 1/2.
The idea that "tails is now more likely to balance things" is the gambler’s fallacy. (If, however, you did not trust the coin to be fair, seeing five heads might reasonably make you suspect a biased coin — in that case a Bayesian update could change your prediction. But with a known fair coin, each flip is 50/50.)
Coin flips are independent events, so the outcome of the sixth flip does not depend on the first five. For a fair coin
- P(tail on 6th | first five were heads) = P(tail on 6th) = 1/2.
The idea that "tails is now more likely to balance things" is the gambler’s fallacy. (If, however, you did not trust the coin to be fair, seeing five heads might reasonably make you suspect a biased coin — in that case a Bayesian update could change your prediction. But with a known fair coin, each flip is 50/50.)
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